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Spectral Networks and Locally Connected Networks on Graphs

arXiv 1312.6203 ↗First posted 21 Dec 2013cs.LG cs.CV cs.NEcited by 1,097

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Abstract (arXiv)

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.

Key facts. Cited by 1,097 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Dec 2013.

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Citing papers per year: 2020: 1; 2021: 297; 2022: 268; 2023: 201; 2024: 163; 2025: 108; 2026: 59.

1,097 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  3. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  4. 2021Channel-wise Topology Refinement Graph Convolution for Skeleton-Based Action Recognitioncited by 317
  5. 2024A Survey on Vision-Language-Action Models for Embodied AIcited by 274
  6. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  7. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  8. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  9. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  10. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  11. 2022Vision GNN: An Image is Worth Graph of Nodescited by 185
  12. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
38 more
  1. 2022Graph neural networks for materials science and chemistrycited by 181
  2. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  3. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  4. 2021Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learningcited by 175
  5. 2021Training Graph Neural Networks with 1000 Layerscited by 169
  6. 2021E(n) Equivariant Normalizing Flowscited by 165
  7. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  8. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  9. 2021Equivariant Subgraph Aggregation Networkscited by 154
  10. 2023Large-scale Multi-Modal Pre-trained Models: A Comprehensive Surveycited by 153
  11. 2021Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillationcited by 151
  12. 2021GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networkscited by 147
  13. 2021Graph Learning: A Surveycited by 140
  14. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  15. 2021Nested Graph Neural Networkscited by 136
  16. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  17. 2022Graph-Coupled Oscillator Networkscited by 123
  18. 2022Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecastingcited by 122
  19. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  20. 2021A Unified Lottery Ticket Hypothesis for Graph Neural Networkscited by 118
  21. 2021DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networkscited by 117
  22. 2021LaneRCNN: Distributed Representations for Graph-Centric Motion Forecastingcited by 112
  23. 2022Towards Unsupervised Deep Graph Structure Learningcited by 112
  24. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  25. 2021MagNet: A Neural Network for Directed Graphscited by 104
  26. 2022How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervisioncited by 102
  27. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  28. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  29. 2021Holistic 3D Scene Understanding from a Single Image with Implicit Representationcited by 94
  30. 2021Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibrationcited by 91
  31. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  32. 2021HDMI: High-order Deep Multiplex Infomaxcited by 82
  33. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  34. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81
  35. 2021Scaling Up Graph Neural Networks Via Graph Coarseningcited by 80
  36. 2021Graph-based Semi-supervised Learning: A Comprehensive Reviewcited by 79
  37. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  38. 2021SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanismcited by 75

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